The Balloon-borne Experiment with a Superconducting Spectrometer (BESS) is configured with a solenoidal superconducting magnet and a suite of precision particle detectors, including time-of-flight hodoscopes based on plastic scintillators, a silica-aerogel Cherenkov detector, and a high resolution tracking system with a central jet-type drift chamber. The charges of incident particles are determined from energy losses in the scintillators. Their magnetic rigidities (momentum charge) are measured by reconstructing each particle trajectory in the magnetic field, and their velocities are obtained by using the time-of-flight system. Together, these measurements can accurately identify helium isotopes among the incoming cosmic-ray helium nuclei up to energies in the GeV per nucleon region. The BESS-Polar I instrument flew for 8.5 days over Antarctica from December 13th to December 21st, 2004. Its long-duration flight and large geometric acceptance allow the time variations of isotopic fluxes to be studied for the first time. The time variations of helium isotope fluxes are presented here for rigidities from 1.2 to 2.5 GV and results are compared to previously reported proton data and neutron monitor data.